1. **State the problem:** Solve the system of inequalities: $$y < -2$$ $$8x + 5y < 30$$ 2. **Understand the inequalities:** - The first inequality means $y$ is less than $-2$. - The second inequality is a linear inequality in $x$ and $y$. 3. **Rewrite the second inequality to express $y$ in terms of $x$:** $$8x + 5y < 30$$ Subtract $8x$ from both sides: $$5y < 30 - 8x$$ Divide both sides by 5 (positive number, so inequality direction stays the same): $$y < \frac{30 - 8x}{5}$$ 4. **Summary of solution region:** $$y < -2$$ and $$y < \frac{30 - 8x}{5}$$ The solution is all points $(x,y)$ where $y$ is less than both $-2$ and $\frac{30 - 8x}{5}$. 5. **Interpretation:** - The region below the horizontal line $y = -2$. - The region below the line $y = \frac{30 - 8x}{5}$. The solution is the intersection of these two regions.